World-of-warcraft – Does the Active Azerite Power Trait ‘Filthy Transfusion’ deal AoE damage

Short answer: Destruction.

Long answer: Given your desire to hit harder and your problems with remembering to cast curses, I would argue that rules out both affliction and demonology. Destruction is going to give you the best DPS output generated from your toon in single hits, which seems to be for what you are yearning. With demonology, your DPS will be split between you and your pet.

If you're the kind of person who likes sheer numbers, you should check out this thread on Elitist Jerks. After running some simulations with SimulationCraft, the following was observed:

• Affliction currently puts out the most DPS, followed by Destruction, then Demonology. This is true for pre-raid or post-raid.
• Destruction outpaces affliction in fights with heavy movement.
• Taking into account the coming PTR changes, it looks like Destruction will outpace Affliction in Tier 11 gear overall.

Yes, you need to use a dagger if you want the bonus damage. Unless otherwise stated, all Rogue abilities use the weapon in your mainhand.

The only two that break from this are Mutilate (uses both hands, simultaneously) and Shiv (which uses only the off-hand)

But -- You're barking up the wrong tree if you're thinking Daggers will cause more damage than other weapons - daggers are unique in having a different (i.e., lower) damage bonus for instant attacks (this is why you don't want to Sinister Strike with a dagger - it'll do less damage than an equivalent iLvl sword, mace, or axe).

Ambush used to be dagger specific. When the ability was updated to be more useful to other specs, they had to do something to make sure ambush wasn't suddenly worst for the dagger specs, hence the extra bonus.

This constant is called the Normalized Weapon speed. WoWpedia has more.